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The motion of three point vortices on a sphere

Abstract

We consider the incompressible and inviscid flow on a sphere. The vorticity distributes as a point vortex. The governing equation for point vortices on a sphere is given by Bogomolov [3]. In the present paper, we study the motion of three point vortices. We prove that the motion is integrable Hamiltonian system and its solution never blows up in finite time. Prom the viewpoint of the configuration of three vortices, we classify the motion with assistance of the numerical computation.

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Sakajo, T. The motion of three point vortices on a sphere. Japan J. Indust. Appl. Math. 16, 321 (1999). https://doi.org/10.1007/BF03167361

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Key words

  • point vortex
  • blow up
  • integrable
  • sphere